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A.5.7: Section 5.7 Answers

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Jan 2, 2021
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- A.5.6: Section 5.6 Answers
- A.6.1: Section 6.1 Answers

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1. $y_{p}=\frac{-\cos 3x\ln |\sec 3x+\tan 3x|}{9}$

2. $y_{p}=-\frac{\sin 2x\ln |\cos 2x|}{4}+\frac{x\cos 2x}{2}$

3. $y_{p} = 4e^{x} (1 + e^{x} ) \ln(1 + e^{−x} )$

4. $y_{p} = 3e^{x} (\cos x \ln | \cos x| + x \sin x)$

5. $y_{p}=\frac{8}{5}x^{7/2}e^{x}$

6. $y_{p}=e^{x}\ln (1-e^{-2x})-e^{-x}\ln (e^{2x}-1)$

7. $y_{p}=\frac{2(x^{2}-3)}{3}$

8. $y_{p}=\frac{e^{2x}}{x}$

9. $y_{p}=x^{1/2}e^{x}\ln x$

10. $y_{p}=e^{-x(x+2)}$

11. $y_{p}=-4x^{5/2}$

12. $y_{p} = −2x^{2} \sin x−2x \cos x$

13. $y_{p}=-\frac{xe^{-x}(x+1)}{2}$

14. $y_{p}=-\frac{\sqrt{x}\cos\sqrt{x}}{2}$

15. $y_{p}=\frac{3x^{4}e^{x}}{2}$

16. $y_{p}=x^{a+1}$

17. $y_{p}=\frac{x^{2}\sin x}{2}$

18. $y_{p}=-2x^{2}$

19. $y_{p}=-e^{-x}\sin x$

20. $y_{p}=-\frac{\sqrt{x}}{2}$

21. $y_{p}=\frac{x^{3/2}}{4}$

22. $y_{p}=-3x^{2}$

23. $y_{p}=\frac{x^{3}e^{x}}{2}$

24. $y_{p}=-\frac{4x^{3/2}}{15}$

25. $y_{p}=x^{3}e^{x}$

26. $y_{p}=xe^{x}$

27. $y_{p}=x^{2}$

28. $y_{p} = xe^{x} (x − 2)$

29. $y_{p}=\sqrt{x}e^{x}(x-1)/4$

30. $y=\frac{e^{2x}(3x^{2}-2x+6)}{6}+\frac{xe^{-x}}{3}$

31. $y = (x − 1)^{2} \ln(1 − x) + 2x^{2} − 5x + 3$

32. $y = (x^{2}−1)e^{x}−5(x−1)$

33. $y=\frac{x(x^{2}+6)}{3(x^{2}-1)}$

34. $y=-\frac{x^{2}}{2}+x+\frac{1}{2x^{2}}$

35. $y=\frac{x^{2}(4x+9)}{6(x+1)}$

38.

$y=k_{0}\cosh x+k_{1}\sinh x+\int _{0}^{x}\sinh (x-t)f(t)dt$
$y'=k_{0}\sinh x+k_{1}\cosh x+\int _{0}^{x}\cosh (x-t)f(t)dt$

39.

$y(x)=k_{0}\cos x+k_{1}\sin x+\int _{0}^{x}\sin (x-t)f(t)dt$
$y'(x)=-k_{0}\sin x+k_{1}\cos x+\int_{0}^{x}\cos (x-t)f(t)dt$

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